Question: Simplify the following expression: $ a = \dfrac{-10t + 4}{-8} + \dfrac{-7}{6} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-10t + 4}{-8} \times \dfrac{6}{6} = \dfrac{-60t + 24}{-48} $ Multiply the second expression by $\dfrac{-8}{-8}$ $ \dfrac{-7}{6} \times \dfrac{-8}{-8} = \dfrac{56}{-48} $ Therefore $ a = \dfrac{-60t + 24}{-48} + \dfrac{56}{-48} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-60t + 24 + 56}{-48} $ $a = \dfrac{-60t + 80}{-48}$ Simplify the expression by dividing the numerator and denominator by -4: $a = \dfrac{15t - 20}{12}$